This sounds like an absolute mess.
Had 3 rooms booked for 2 nights, showed up at 2:30 and kept getting told to come back later because housekeeping was behind. By 8pm the lobby was packed with stranded guests and a softball team. After standing in line for 1.5 hours, you get emails at 9:30pm saying your rooms are canceled. While you’re literally in front of them. With a 7 month old. That’s brutal.
No walk to another hotel, no real communication, nothing.
And now two weeks later you’re still charged for all 3 rooms? That’s the craziest part. That should be a basic, immediate fix.
At this point I’d escalate beyond just calling. If corporate isn’t resolving it, I’d dispute the charge with your credit card while the case is open. You have clear grounds since you were denied the stay. That usually gets attention fast.
As for compensation, at minimum you should get:
Full refund immediately
Reimbursement for the replacement hotel
Some form of points or goodwill credit on top of that
Given the situation, I wouldn’t think asking for a substantial points gesture is unreasonable.
But first priority is getting your money back. Two weeks with no refund on canceled rooms is not normal.
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